Notes 11 addendum Recall : Since the sampling distribution of the sample mean, X ~         = = n X X σ μ , now follows a Normal distribution, we can use the standardizing formula n x x z X X − = − = to find z-scores for sample mean calculations. Example 1 : IQ scores of college students are Normally distributed with mean 120 and standard deviation 9. (a) State the distribution of X = the IQ score of a randomly selected student ? (b) What is the z-score formula for X? (c) What is the distribution of X = the average IQ score of 10 randomly selected students ? (d) What is the z-score formula for X ? Example 2 : If the random variable X represents the height of a randomly selected woman, then X is normally distributed with a mean of 63.5 = inches and a population standard deviation of 2.75 = inches. Suppose a random sample of 16 women is selected, find the probability of selecting a

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Unformatted text preview: sample of women whose average height is more than 65 inches. &ote : We have already learned how to calculate the probability that a randomly selected woman’s height is greater than 65 inches tall. &ow we are trying to find the probability of a women’s average height being greater than 65 inches tall. Notes 11 addendum Example 3 : The weight of potato chips in a bag is stated as 11oz. The amounts that the packing machine actually puts in these bags varies with mean 10.1 oz and standard deviation 0.23 oz. (a) Write down the distribution of X = the mean weight of a sample of 50 bags of potato chips. (b) What is the probability that the mean weight of 50 bags will be below 10 oz? (c) There is a 0.7 probability that the mean weight of 50 bags is above a certain amount. What is that amount?...
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